Question : The difference between the compound interest and the simple interest on a certain sum of money at 10% per annum for 2 years is INR 200. What is the sum of money, if in the case of compound interest, interest is compounded annually?
Option 1: INR 25,000
Option 2: INR 15,000
Option 3: INR 12,000
Option 4: INR 20,000
Correct Answer: INR 20,000
Solution :
Given: The difference between the compound interest and the simple interest on a certain sum of money at 10% per annum for 2 years is INR 200.
Use the formula, $CI–SI=P(\frac{R}{100})^T$ where $SI$, $CI$, $R$, $T$ are the simple interest, compound interest, rate, and time.
According to the question,
$200=P(\frac{10}{100})^2$
⇒ $200=P(\frac{1}{10})^2$
⇒ $200=P\times\frac{1}{100}$
⇒ $P=$ INR 20,000
Hence, the correct answer is INR 20,000.
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